LMFDB - Embedded newform 1155.2.c.c.694.3

Show commands: Magma / PariGP / SageMath

Newspace parameters

comment: Compute space of new eigenforms

[N,k,chi] = [1155,2,Mod(694,1155)]

mf = mfinit([N,k,chi],0)

lf = mfeigenbasis(mf)

from sage.modular.dirichlet import DirichletCharacter

H = DirichletGroup(1155, base_ring=CyclotomicField(2))

chi = DirichletCharacter(H, H._module([0, 1, 0, 0]))

N = Newforms(chi, 2, names="a")

//Please install CHIMP (https://github.com/edgarcosta/CHIMP) if you want to run this code

chi := DirichletCharacter("1155.694");

S:= CuspForms(chi, 2);

N := Newforms(S);

Level:	$ N $	$=$	$ 1155 = 3 \cdot 5 \cdot 7 \cdot 11 $
Weight:	$ k $	$=$	$ 2 $
Character orbit:	$[\chi]$	$=$	1155.c (of order $2$, degree $1$, minimal)

Newform invariants

comment: select newform

sage: f = N[0] # Warning: the index may be different

gp: f = lf[1] \\ Warning: the index may be different

Self dual:	no
Analytic conductor:	$9.22272143346$
Analytic rank:	$0$
Dimension:	$6$
Coefficient field:	6.0.350464.1
comment: defining polynomial gp: f.mod \\ as an extension of the character field
Defining polynomial:	$ x^{6} - 2x^{5} + 2x^{4} + 2x^{3} + 4x^{2} - 4x + 2 $ x^6 - 2x^5 + 2x^4 + 2x^3 + 4x^2 - 4*x + 2
Coefficient ring:	$\Z[a_1, a_2, a_3]$
Coefficient ring index:	$ 2 $
Twist minimal:	yes
Sato-Tate group:	$\mathrm{SU}(2)[C_{2}]$

Embedding invariants

Embedding label			694.3
Root			$-0.854638 + 0.854638i$ of defining polynomial
Character	$\chi$	$=$	1155.694
Dual form			1155.2.c.c.694.4

$q$-expansion

comment: q-expansion

sage: f.q_expansion() # note that sage often uses an isomorphic number field

gp: mfcoefs(f, 20)

$f(q)$	$=$	$q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +0.539189 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})$	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +0.539189 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(-0.290725 - 1.17009i) q^{10} -1.00000 q^{11} +1.70928i q^{12} +3.17009i q^{13} +0.539189 q^{14} +(0.539189 + 2.17009i) q^{15} +2.34017 q^{16} +2.70928i q^{17} +0.539189i q^{18} +3.34017 q^{19} +(3.70928 - 0.921622i) q^{20} -1.00000 q^{21} +0.539189i q^{22} +1.63090i q^{23} +2.00000 q^{24} +(4.41855 - 2.34017i) q^{25} +1.70928 q^{26} -1.00000i q^{27} +1.70928i q^{28} -1.24846 q^{29} +(1.17009 - 0.290725i) q^{30} +5.21953 q^{31} -5.26180i q^{32} -1.00000i q^{33} +1.46081 q^{34} +(0.539189 + 2.17009i) q^{35} -1.70928 q^{36} +3.17009i q^{37} -1.80098i q^{38} -3.17009 q^{39} +(-1.07838 - 4.34017i) q^{40} -0.829914 q^{41} +0.539189i q^{42} -1.24846i q^{43} -1.70928 q^{44} +(-2.17009 + 0.539189i) q^{45} +0.879362 q^{46} -4.87936i q^{47} +2.34017i q^{48} -1.00000 q^{49} +(-1.26180 - 2.38243i) q^{50} -2.70928 q^{51} +5.41855i q^{52} -5.92162i q^{53} -0.539189 q^{54} +(-2.17009 + 0.539189i) q^{55} +2.00000 q^{56} +3.34017i q^{57} +0.673158i q^{58} +4.46081 q^{59} +(0.921622 + 3.70928i) q^{60} -7.44748 q^{61} -2.81432i q^{62} -1.00000i q^{63} +1.84324 q^{64} +(1.70928 + 6.87936i) q^{65} -0.539189 q^{66} +2.00000i q^{67} +4.63090i q^{68} -1.63090 q^{69} +(1.17009 - 0.290725i) q^{70} -11.6670 q^{71} +2.00000i q^{72} +6.92162i q^{73} +1.70928 q^{74} +(2.34017 + 4.41855i) q^{75} +5.70928 q^{76} -1.00000i q^{77} +1.70928i q^{78} -9.21953 q^{79} +(5.07838 - 1.26180i) q^{80} +1.00000 q^{81} +0.447480i q^{82} -15.0494i q^{83} -1.70928 q^{84} +(1.46081 + 5.87936i) q^{85} -0.673158 q^{86} -1.24846i q^{87} +2.00000i q^{88} +11.4319 q^{89} +(0.290725 + 1.17009i) q^{90} -3.17009 q^{91} +2.78765i q^{92} +5.21953i q^{93} -2.63090 q^{94} +(7.24846 - 1.80098i) q^{95} +5.26180 q^{96} +4.32684i q^{97} +0.539189i q^{98} +1.00000 q^{99} +O(q^{100})\)
$\operatorname{Tr}(f)(q)$	$=$	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	$ 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} - 16 q^{10} - 6 q^{11} - 8 q^{16} - 2 q^{19} + 8 q^{20} - 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{29} - 4 q^{30} - 16 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{55} + 12 q^{56} + 30 q^{59} + 12 q^{60} - 46 q^{61} + 24 q^{64} - 4 q^{65} - 2 q^{69} - 4 q^{70} - 24 q^{71} - 4 q^{74} - 8 q^{75} + 20 q^{76} - 8 q^{79} + 24 q^{80} + 6 q^{81} + 4 q^{84} + 12 q^{85} - 28 q^{86} + 42 q^{89} + 16 q^{90} - 8 q^{91} - 8 q^{94} + 26 q^{95} + 16 q^{96} + 6 q^{99}+O(q^{100}) $ 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 - 16 * q^10 - 6 * q^11 - 8 * q^16 - 2 * q^19 + 8 * q^20 - 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^29 - 4 * q^30 - 16 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^55 + 12 * q^56 + 30 * q^59 + 12 * q^60 - 46 * q^61 + 24 * q^64 - 4 * q^65 - 2 * q^69 - 4 * q^70 - 24 * q^71 - 4 * q^74 - 8 * q^75 + 20 * q^76 - 8 * q^79 + 24 * q^80 + 6 * q^81 + 4 * q^84 + 12 * q^85 - 28 * q^86 + 42 * q^89 + 16 * q^90 - 8 * q^91 - 8 * q^94 + 26 * q^95 + 16 * q^96 + 6 * q^99

Display 100 coefficients 10 coefficients

Character values

We give the values of $\chi$ on generators for $\left(\mathbb{Z}/1155\mathbb{Z}\right)^\times$.

$n$	$211$	$232$	$386$	$661$
$\chi(n)$	$1$	$-1$	$1$	$1$

Coefficient data

For each $n$ we display the coefficients of the $q$-expansion $a_n$, the Satake parameters $\alpha_p$, and the Satake angles $\theta_p = \textrm{Arg}(\alpha_p)$.

Display $a_p$ with $p$ up to: 50 250 1000 (See $a_n$ instead) (See $a_n$ instead) (See $a_n$ instead) Display $a_n$ with $n$ up to: 50 250 1000 (See only $a_p$) (See only $a_p$) (See only $a_p$)

$n$	$a_n$			$a_n / n^{(k-1)/2}$			$ \alpha_n $			$ \theta_n $
$p$	$a_p$			$a_p / p^{(k-1)/2}$			$ \alpha_p$			$ \theta_p $

$2$		−	0.539189i		−	0.381264i	−0.981662	−	0.190632i	$-0.938946\pi$
$2$		−	0.539189i		−	0.381264i	0.981662	−	0.190632i	$-0.0610537\pi$
$3$			1.00000i			0.577350i
$3$			1.00000i			0.577350i
$4$	1.70928			0.854638
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$5$	2.17009	−	0.539189i	0.970492	−	0.241133i
$6$	0.539189			0.220123
$7$			1.00000i			0.377964i
$7$			1.00000i			0.377964i
$8$		−	2.00000i		−	0.707107i
$9$	−1.00000			−0.333333
$10$	−0.290725	−	1.17009i	−0.0919352	−	0.370014i
$11$	−1.00000			−0.301511
$11$	−1.00000			−0.301511
$12$			1.70928i			0.493425i
$13$			3.17009i			0.879224i	0.898188	+	0.439612i	$0.144884\pi$
$13$			3.17009i			0.879224i	−0.898188	+	0.439612i	$0.855116\pi$
$14$	0.539189			0.144104
$15$	0.539189	+	2.17009i	0.139218	+	0.560314i
$16$	2.34017			0.585043
$17$			2.70928i			0.657096i	0.944487	+	0.328548i	$0.106559\pi$
$17$			2.70928i			0.657096i	−0.944487	+	0.328548i	$0.893441\pi$
$18$			0.539189i			0.127088i
$19$	3.34017			0.766288			0.383144	−	0.923689i	$-0.374841\pi$
$19$	3.34017			0.766288			0.383144	+	0.923689i	$0.374841\pi$
$20$	3.70928	−	0.921622i	0.829419	−	0.206081i
$21$	−1.00000			−0.218218
$22$			0.539189i			0.114955i
$23$			1.63090i			0.340066i	0.985438	+	0.170033i	$0.0543874\pi$
$23$			1.63090i			0.340066i	−0.985438	+	0.170033i	$0.945613\pi$
$24$	2.00000			0.408248
$25$	4.41855	−	2.34017i	0.883710	−	0.468035i
$26$	1.70928			0.335216
$27$		−	1.00000i		−	0.192450i
$28$			1.70928i			0.323023i
$29$	−1.24846			−0.231834			−0.115917	−	0.993259i	$-0.536981\pi$
$29$	−1.24846			−0.231834			−0.115917	+	0.993259i	$0.536981\pi$
$30$	1.17009	−	0.290725i	0.213628	−	0.0530788i
$31$	5.21953			0.937456			0.468728	−	0.883343i	$-0.344712\pi$
$31$	5.21953			0.937456			0.468728	+	0.883343i	$0.344712\pi$
$32$		−	5.26180i		−	0.930163i
$33$		−	1.00000i		−	0.174078i
$34$	1.46081			0.250527
$35$	0.539189	+	2.17009i	0.0911396	+	0.366812i
$36$	−1.70928			−0.284879
$37$			3.17009i			0.521159i	0.965452	+	0.260580i	$0.0839136\pi$
$37$			3.17009i			0.521159i	−0.965452	+	0.260580i	$0.916086\pi$
$38$		−	1.80098i		−	0.292158i
$39$	−3.17009			−0.507620
$40$	−1.07838	−	4.34017i	−0.170506	−	0.686242i
$41$	−0.829914			−0.129611			−0.0648054	−	0.997898i	$-0.520643\pi$
$41$	−0.829914			−0.129611			−0.0648054	+	0.997898i	$0.520643\pi$
$42$			0.539189i			0.0831986i
$43$		−	1.24846i		−	0.190389i	−0.995459	−	0.0951945i	$-0.969653\pi$
$43$		−	1.24846i		−	0.190389i	0.995459	−	0.0951945i	$-0.0303473\pi$
$44$	−1.70928			−0.257683
$45$	−2.17009	+	0.539189i	−0.323497	+	0.0803775i
$46$	0.879362			0.129655
$47$		−	4.87936i		−	0.711728i	−0.934538	−	0.355864i	$-0.884187\pi$
$47$		−	4.87936i		−	0.711728i	0.934538	−	0.355864i	$-0.115813\pi$
$48$			2.34017i			0.337775i
$49$	−1.00000			−0.142857
$50$	−1.26180	−	2.38243i	−0.178445	−	0.336927i
$51$	−2.70928			−0.379374
$52$			5.41855i			0.751418i
$53$		−	5.92162i		−	0.813397i	−0.913562	−	0.406699i	$-0.866680\pi$
$53$		−	5.92162i		−	0.813397i	0.913562	−	0.406699i	$-0.133320\pi$
$54$	−0.539189			−0.0733743
$55$	−2.17009	+	0.539189i	−0.292614	+	0.0727042i
$56$	2.00000			0.267261
$57$			3.34017i			0.442417i
$58$			0.673158i			0.0883900i
$59$	4.46081			0.580748			0.290374	−	0.956913i	$-0.406220\pi$
$59$	4.46081			0.580748			0.290374	+	0.956913i	$0.406220\pi$
$60$	0.921622	+	3.70928i	0.118981	+	0.478865i
$61$	−7.44748			−0.953552			−0.476776	−	0.879025i	$-0.658195\pi$
$61$	−7.44748			−0.953552			−0.476776	+	0.879025i	$0.658195\pi$
$62$		−	2.81432i		−	0.357418i
$63$		−	1.00000i		−	0.125988i
$64$	1.84324			0.230406
$65$	1.70928	+	6.87936i	0.212010	+	0.853280i
$66$	−0.539189			−0.0663696
$67$			2.00000i			0.244339i	0.992509	+	0.122169i	$0.0389851\pi$
$67$			2.00000i			0.244339i	−0.992509	+	0.122169i	$0.961015\pi$
$68$			4.63090i			0.561579i
$69$	−1.63090			−0.196337
$70$	1.17009	−	0.290725i	0.139852	−	0.0347482i
$71$	−11.6670			−1.38462			−0.692310	−	0.721600i	$-0.743407\pi$
$71$	−11.6670			−1.38462			−0.692310	+	0.721600i	$0.743407\pi$
$72$			2.00000i			0.235702i
$73$			6.92162i			0.810115i	0.914291	+	0.405057i	$0.132748\pi$
$73$			6.92162i			0.810115i	−0.914291	+	0.405057i	$0.867252\pi$
$74$	1.70928			0.198699
$75$	2.34017	+	4.41855i	0.270220	+	0.510210i
$76$	5.70928			0.654899
$77$		−	1.00000i		−	0.113961i
$78$			1.70928i			0.193537i
$79$	−9.21953			−1.03728			−0.518639	−	0.854993i	$-0.673561\pi$
$79$	−9.21953			−1.03728			−0.518639	+	0.854993i	$0.673561\pi$
$80$	5.07838	−	1.26180i	0.567780	−	0.141073i
$81$	1.00000			0.111111
$82$			0.447480i			0.0494159i
$83$		−	15.0494i		−	1.65189i	−0.563750	−	0.825946i	$-0.690642\pi$
$83$		−	15.0494i		−	1.65189i	0.563750	−	0.825946i	$-0.309358\pi$
$84$	−1.70928			−0.186497
$85$	1.46081	+	5.87936i	0.158447	+	0.637706i
$86$	−0.673158			−0.0725885
$87$		−	1.24846i		−	0.133849i
$88$			2.00000i			0.213201i
$89$	11.4319			1.21178			0.605889	−	0.795550i	$-0.292818\pi$
$89$	11.4319			1.21178			0.605889	+	0.795550i	$0.292818\pi$
$90$	0.290725	+	1.17009i	0.0306451	+	0.123338i
$91$	−3.17009			−0.332315
$92$			2.78765i			0.290633i
$93$			5.21953i			0.541241i
$94$	−2.63090			−0.271356
$95$	7.24846	−	1.80098i	0.743677	−	0.184777i
$96$	5.26180			0.537030
$97$			4.32684i			0.439324i	0.975576	+	0.219662i	$0.0704955\pi$
$97$			4.32684i			0.439324i	−0.975576	+	0.219662i	$0.929505\pi$
$98$			0.539189i			0.0544663i
$99$	1.00000			0.100504
$100$	7.55252	−	4.00000i	0.755252	−	0.400000i
$101$	2.68035			0.266704			0.133352	−	0.991069i	$-0.457426\pi$
$101$	2.68035			0.266704			0.133352	+	0.991069i	$0.457426\pi$
$102$			1.46081i			0.144642i
$103$		−	9.00719i		−	0.887505i	−0.896149	−	0.443752i	$-0.853647\pi$
$103$		−	9.00719i		−	0.887505i	0.896149	−	0.443752i	$-0.146353\pi$
$104$	6.34017			0.621705
$105$	−2.17009	+	0.539189i	−0.211779	+	0.0526194i
$106$	−3.19287			−0.310119
$107$			9.80098i			0.947497i	0.880660	+	0.473748i	$0.157099\pi$
$107$			9.80098i			0.947497i	−0.880660	+	0.473748i	$0.842901\pi$
$108$		−	1.70928i		−	0.164475i
$109$	12.2979			1.17793			0.588963	−	0.808160i	$-0.299536\pi$
$109$	12.2979			1.17793			0.588963	+	0.808160i	$0.299536\pi$
$110$	0.290725	+	1.17009i	0.0277195	+	0.111563i
$111$	−3.17009			−0.300891
$112$			2.34017i			0.221126i
$113$		−	12.8660i		−	1.21033i	−0.796098	−	0.605167i	$-0.793106\pi$
$113$		−	12.8660i		−	1.21033i	0.796098	−	0.605167i	$-0.206894\pi$
$114$	1.80098			0.168678
$115$	0.879362	+	3.53919i	0.0820009	+	0.330031i
$116$	−2.13397			−0.198134
$117$		−	3.17009i		−	0.293075i
$118$		−	2.40522i		−	0.221418i
$119$	−2.70928			−0.248359
$120$	4.34017	−	1.07838i	0.396202	−	0.0984420i
$121$	1.00000			0.0909091
$122$			4.01560i			0.363555i
$123$		−	0.829914i		−	0.0748308i
$124$	8.92162			0.801185
$125$	8.32684	−	7.46081i	0.744775	−	0.667315i
$126$	−0.539189			−0.0480348
$127$			7.14116i			0.633675i	0.948480	+	0.316838i	$0.102621\pi$
$127$			7.14116i			0.633675i	−0.948480	+	0.316838i	$0.897379\pi$
$128$		−	11.5174i		−	1.01801i
$129$	1.24846			0.109921
$130$	3.70928	−	0.921622i	0.325325	−	0.0808316i
$131$	−2.09171			−0.182753			−0.0913767	−	0.995816i	$-0.529127\pi$
$131$	−2.09171			−0.182753			−0.0913767	+	0.995816i	$0.529127\pi$
$132$		−	1.70928i		−	0.148773i
$133$			3.34017i			0.289630i
$134$	1.07838			0.0931576
$135$	−0.539189	−	2.17009i	−0.0464060	−	0.186771i
$136$	5.41855			0.464637
$137$		−	11.2846i		−	0.964107i	−0.876142	−	0.482053i	$-0.839891\pi$
$137$		−	11.2846i		−	0.964107i	0.876142	−	0.482053i	$-0.160109\pi$
$138$			0.879362i			0.0748563i
$139$	−19.9916			−1.69566			−0.847832	−	0.530265i	$-0.822093\pi$
$139$	−19.9916			−1.69566			−0.847832	+	0.530265i	$0.822093\pi$
$140$	0.921622	+	3.70928i	0.0778913	+	0.313491i
$141$	4.87936			0.410916
$142$			6.29072i			0.527906i
$143$		−	3.17009i		−	0.265096i
$144$	−2.34017			−0.195014
$145$	−2.70928	+	0.673158i	−0.224993	+	0.0559027i
$146$	3.73206			0.308868
$147$		−	1.00000i		−	0.0824786i
$148$			5.41855i			0.445402i
$149$	−10.0000			−0.819232			−0.409616	−	0.912258i	$-0.634337\pi$
$149$	−10.0000			−0.819232			−0.409616	+	0.912258i	$0.634337\pi$
$150$	2.38243	−	1.26180i	0.194525	−	0.103025i
$151$	−3.26180			−0.265441			−0.132721	−	0.991153i	$-0.542371\pi$
$151$	−3.26180			−0.265441			−0.132721	+	0.991153i	$0.542371\pi$
$152$		−	6.68035i		−	0.541848i
$153$		−	2.70928i		−	0.219032i
$154$	−0.539189			−0.0434491
$155$	11.3268	−	2.81432i	0.909794	−	0.226051i
$156$	−5.41855			−0.433831
$157$			8.06278i			0.643480i	0.946828	+	0.321740i	$0.104268\pi$
$157$			8.06278i			0.643480i	−0.946828	+	0.321740i	$0.895732\pi$
$158$			4.97107i			0.395477i
$159$	5.92162			0.469615
$160$	−2.83710	−	11.4186i	−0.224293	−	0.902716i
$161$	−1.63090			−0.128533
$162$		−	0.539189i		−	0.0423627i
$163$			3.17009i			0.248300i	0.992263	+	0.124150i	$0.0396205\pi$
$163$			3.17009i			0.248300i	−0.992263	+	0.124150i	$0.960380\pi$
$164$	−1.41855			−0.110770
$165$	−0.539189	−	2.17009i	−0.0419758	−	0.168941i
$166$	−8.11450			−0.629807
$167$		−	4.20620i		−	0.325486i	−0.986669	−	0.162743i	$-0.947966\pi$
$167$		−	4.20620i		−	0.325486i	0.986669	−	0.162743i	$-0.0520341\pi$
$168$			2.00000i			0.154303i
$169$	2.95055			0.226966
$170$	3.17009	−	0.787653i	0.243135	−	0.0604102i
$171$	−3.34017			−0.255429
$172$		−	2.13397i		−	0.162714i
$173$			2.65756i			0.202051i	0.994884	+	0.101025i	$0.0322123\pi$
$173$			2.65756i			0.202051i	−0.994884	+	0.101025i	$0.967788\pi$
$174$	−0.673158			−0.0510320
$175$	2.34017	+	4.41855i	0.176900	+	0.334011i
$176$	−2.34017			−0.176397
$177$			4.46081i			0.335295i
$178$		−	6.16394i		−	0.462007i
$179$	−19.3679			−1.44762			−0.723812	−	0.689998i	$-0.757612\pi$
$179$	−19.3679			−1.44762			−0.723812	+	0.689998i	$0.757612\pi$
$180$	−3.70928	+	0.921622i	−0.276473	+	0.0686937i
$181$	−10.7070			−0.795846			−0.397923	−	0.917419i	$-0.630269\pi$
$181$	−10.7070			−0.795846			−0.397923	+	0.917419i	$0.630269\pi$
$182$			1.70928i			0.126700i
$183$		−	7.44748i		−	0.550534i
$184$	3.26180			0.240463
$185$	1.70928	+	6.87936i	0.125668	+	0.505781i
$186$	2.81432			0.206356
$187$		−	2.70928i		−	0.198122i
$188$		−	8.34017i		−	0.608270i
$189$	1.00000			0.0727393
$190$	−0.971071	−	3.90829i	−0.0704489	−	0.283537i
$191$	−18.6225			−1.34748			−0.673738	−	0.738970i	$-0.735312\pi$
$191$	−18.6225			−1.34748			−0.673738	+	0.738970i	$0.735312\pi$
$192$			1.84324i			0.133025i
$193$			14.7792i			1.06383i	0.846797	+	0.531917i	$0.178528\pi$
$193$			14.7792i			1.06383i	−0.846797	+	0.531917i	$0.821472\pi$
$194$	2.33299			0.167499
$195$	−6.87936	+	1.70928i	−0.492641	+	0.122404i
$196$	−1.70928			−0.122091
$197$			19.0928i			1.36030i	0.733072	+	0.680151i	$0.238086\pi$
$197$			19.0928i			1.36030i	−0.733072	+	0.680151i	$0.761914\pi$
$198$		−	0.539189i		−	0.0383185i
$199$	24.4391			1.73244			0.866220	−	0.499663i	$-0.166543\pi$
$199$	24.4391			1.73244			0.866220	+	0.499663i	$0.166543\pi$
$200$	−4.68035	−	8.83710i	−0.330950	−	0.624877i
$201$	−2.00000			−0.141069
$202$		−	1.44521i		−	0.101685i
$203$		−	1.24846i		−	0.0876250i
$204$	−4.63090			−0.324228
$205$	−1.80098	+	0.447480i	−0.125786	+	0.0312534i
$206$	−4.85658			−0.338374
$207$		−	1.63090i		−	0.113355i
$208$			7.41855i			0.514384i
$209$	−3.34017			−0.231045
$210$	0.290725	+	1.17009i	0.0200619	+	0.0807436i
$211$	−22.2557			−1.53214			−0.766071	−	0.642756i	$-0.777791\pi$
$211$	−22.2557			−1.53214			−0.766071	+	0.642756i	$0.777791\pi$
$212$		−	10.1217i		−	0.695160i
$213$		−	11.6670i		−	0.799411i
$214$	5.28458			0.361247
$215$	−0.673158	−	2.70928i	−0.0459090	−	0.184771i
$216$	−2.00000			−0.136083
$217$			5.21953i			0.354325i
$218$		−	6.63090i		−	0.449101i
$219$	−6.92162			−0.467720
$220$	−3.70928	+	0.921622i	−0.250079	+	0.0621358i
$221$	−8.58864			−0.577734
$222$			1.70928i			0.114719i
$223$		−	24.1845i		−	1.61951i	−0.586767	−	0.809756i	$-0.699600\pi$
$223$		−	24.1845i		−	1.61951i	0.586767	−	0.809756i	$-0.300400\pi$
$224$	5.26180			0.351568
$225$	−4.41855	+	2.34017i	−0.294570	+	0.156012i
$226$	−6.93722			−0.461457
$227$		−	25.9360i		−	1.72143i	−0.509085	−	0.860716i	$-0.670016\pi$
$227$		−	25.9360i		−	1.72143i	0.509085	−	0.860716i	$-0.329984\pi$
$228$			5.70928i			0.378106i
$229$	−0.937221			−0.0619333			−0.0309666	−	0.999520i	$-0.509859\pi$
$229$	−0.937221			−0.0619333			−0.0309666	+	0.999520i	$0.509859\pi$
$230$	1.90829	−	0.474142i	0.125829	−	0.0312640i
$231$	1.00000			0.0657952
$232$			2.49693i			0.163931i
$233$			17.4752i			1.14484i	0.819961	+	0.572419i	$0.193995\pi$
$233$			17.4752i			1.14484i	−0.819961	+	0.572419i	$0.806005\pi$
$234$	−1.70928			−0.111739
$235$	−2.63090	−	10.5886i	−0.171621	−	0.690727i
$236$	7.62475			0.496329
$237$		−	9.21953i		−	0.598873i
$238$			1.46081i			0.0946903i
$239$	−13.0423			−0.843634			−0.421817	−	0.906681i	$-0.638607\pi$
$239$	−13.0423			−0.843634			−0.421817	+	0.906681i	$0.638607\pi$
$240$	1.26180	+	5.07838i	0.0814485	+	0.327808i
$241$	−18.6042			−1.19840			−0.599202	−	0.800598i	$-0.704515\pi$
$241$	−18.6042			−1.19840			−0.599202	+	0.800598i	$0.704515\pi$
$242$		−	0.539189i		−	0.0346604i
$243$			1.00000i			0.0641500i
$244$	−12.7298			−0.814942
$245$	−2.17009	+	0.539189i	−0.138642	+	0.0344475i
$246$	−0.447480			−0.0285303
$247$			10.5886i			0.673739i
$248$		−	10.4391i		−	0.662882i
$249$	15.0494			0.953720
$250$	−4.02279	−	4.48974i	−0.254423	−	0.283956i
$251$	−2.21008			−0.139499			−0.0697495	−	0.997565i	$-0.522220\pi$
$251$	−2.21008			−0.139499			−0.0697495	+	0.997565i	$0.522220\pi$
$252$		−	1.70928i		−	0.107674i
$253$		−	1.63090i		−	0.102534i
$254$	3.85043			0.241598
$255$	−5.87936	+	1.46081i	−0.368180	+	0.0914795i
$256$	−2.52359			−0.157724
$257$			1.20516i			0.0751758i	0.999293	+	0.0375879i	$0.0119674\pi$
$257$			1.20516i			0.0751758i	−0.999293	+	0.0375879i	$0.988033\pi$
$258$		−	0.673158i		−	0.0419090i
$259$	−3.17009			−0.196980
$260$	2.92162	+	11.7587i	0.181191	+	0.729245i
$261$	1.24846			0.0772780
$262$			1.12783i			0.0696773i
$263$		−	11.8432i		−	0.730286i	−0.930951	−	0.365143i	$-0.881020\pi$
$263$		−	11.8432i		−	0.730286i	0.930951	−	0.365143i	$-0.118980\pi$
$264$	−2.00000			−0.123091
$265$	−3.19287	−	12.8504i	−0.196137	−	0.789396i
$266$	1.80098			0.110425
$267$			11.4319i			0.699620i
$268$			3.41855i			0.208821i
$269$	23.5802			1.43771			0.718856	−	0.695159i	$-0.244666\pi$
$269$	23.5802			1.43771			0.718856	+	0.695159i	$0.244666\pi$
$270$	−1.17009	+	0.290725i	−0.0712092	+	0.0176929i
$271$	−9.99773			−0.607319			−0.303660	−	0.952781i	$-0.598209\pi$
$271$	−9.99773			−0.607319			−0.303660	+	0.952781i	$0.598209\pi$
$272$			6.34017i			0.384429i
$273$		−	3.17009i		−	0.191862i
$274$	−6.08452			−0.367579
$275$	−4.41855	+	2.34017i	−0.266449	+	0.141118i
$276$	−2.78765			−0.167797
$277$		−	29.8660i		−	1.79448i	−0.441547	−	0.897238i	$-0.645570\pi$
$277$		−	29.8660i		−	1.79448i	0.441547	−	0.897238i	$-0.354430\pi$
$278$			10.7792i			0.646496i
$279$	−5.21953			−0.312485
$280$	4.34017	−	1.07838i	0.259375	−	0.0644454i
$281$	−17.8660			−1.06580			−0.532899	−	0.846179i	$-0.678897\pi$
$281$	−17.8660			−1.06580			−0.532899	+	0.846179i	$0.678897\pi$
$282$		−	2.63090i		−	0.156668i
$283$		−	4.56198i		−	0.271181i	−0.990765	−	0.135591i	$-0.956707\pi$
$283$		−	4.56198i		−	0.271181i	0.990765	−	0.135591i	$-0.0432932\pi$
$284$	−19.9421			−1.18335
$285$	1.80098	+	7.24846i	0.106681	+	0.429362i
$286$	−1.70928			−0.101072
$287$		−	0.829914i		−	0.0489882i
$288$			5.26180i			0.310054i
$289$	9.65983			0.568225
$290$	0.362959	+	1.46081i	0.0213137	+	0.0857818i
$291$	−4.32684			−0.253644
$292$			11.8310i			0.692354i
$293$		−	15.0144i		−	0.877149i	−0.898695	−	0.438575i	$-0.855483\pi$
$293$		−	15.0144i		−	0.877149i	0.898695	−	0.438575i	$-0.144517\pi$
$294$	−0.539189			−0.0314461
$295$	9.68035	−	2.40522i	0.563612	−	0.140037i
$296$	6.34017			0.368515
$297$			1.00000i			0.0580259i
$298$			5.39189i			0.312344i
$299$	−5.17009			−0.298994
$300$	4.00000	+	7.55252i	0.230940	+	0.436045i
$301$	1.24846			0.0719603
$302$			1.75872i			0.101203i
$303$			2.68035i			0.153982i
$304$	7.81658			0.448312
$305$	−16.1617	+	4.01560i	−0.925415	+	0.229932i
$306$	−1.46081			−0.0835090
$307$		−	20.6537i		−	1.17877i	−0.807853	−	0.589384i	$-0.799371\pi$
$307$		−	20.6537i		−	1.17877i	0.807853	−	0.589384i	$-0.200629\pi$
$308$		−	1.70928i		−	0.0973950i
$309$	9.00719			0.512401
$310$	−1.51745	−	6.10731i	−0.0861852	−	0.346872i
$311$	−23.1506			−1.31275			−0.656375	−	0.754434i	$-0.727911\pi$
$311$	−23.1506			−1.31275			−0.656375	+	0.754434i	$0.727911\pi$
$312$			6.34017i			0.358942i
$313$			25.9516i			1.46687i	0.679759	+	0.733435i	$0.262084\pi$
$313$			25.9516i			1.46687i	−0.679759	+	0.733435i	$0.737916\pi$
$314$	4.34736			0.245336
$315$	−0.539189	−	2.17009i	−0.0303799	−	0.122271i
$316$	−15.7587			−0.886497
$317$			7.06997i			0.397089i	0.980092	+	0.198544i	$0.0636214\pi$
$317$			7.06997i			0.397089i	−0.980092	+	0.198544i	$0.936379\pi$
$318$		−	3.19287i		−	0.179047i
$319$	1.24846			0.0699006
$320$	4.00000	−	0.993857i	0.223607	−	0.0555583i
$321$	−9.80098			−0.547038
$322$			0.879362i			0.0490049i
$323$			9.04945i			0.503525i
$324$	1.70928			0.0949597
$325$	7.41855	+	14.0072i	0.411507	+	0.776979i
$326$	1.70928			0.0946680
$327$			12.2979i			0.680076i
$328$			1.65983i			0.0916486i
$329$	4.87936			0.269008
$330$	−1.17009	+	0.290725i	−0.0644111	+	0.0160039i
$331$	1.26794			0.0696922			0.0348461	−	0.999393i	$-0.488906\pi$
$331$	1.26794			0.0696922			0.0348461	+	0.999393i	$0.488906\pi$
$332$		−	25.7237i		−	1.41177i
$333$		−	3.17009i		−	0.173720i
$334$	−2.26794			−0.124096
$335$	1.07838	+	4.34017i	0.0589181	+	0.237129i
$336$	−2.34017			−0.127667
$337$			2.51026i			0.136743i	0.997660	+	0.0683713i	$0.0217802\pi$
$337$			2.51026i			0.136743i	−0.997660	+	0.0683713i	$0.978220\pi$
$338$		−	1.59090i		−	0.0865338i
$339$	12.8660			0.698787
$340$	2.49693	+	10.0494i	0.135415	+	0.545008i
$341$	−5.21953			−0.282654
$342$			1.80098i			0.0973861i
$343$		−	1.00000i		−	0.0539949i
$344$	−2.49693			−0.134625
$345$	−3.53919	+	0.879362i	−0.190544	+	0.0473433i
$346$	1.43293			0.0770346
$347$			1.68649i			0.0905355i	0.998975	+	0.0452677i	$0.0144141\pi$
$347$			1.68649i			0.0905355i	−0.998975	+	0.0452677i	$0.985586\pi$
$348$		−	2.13397i		−	0.114393i
$349$	33.5113			1.79382			0.896909	−	0.442214i	$-0.145807\pi$
$349$	33.5113			1.79382			0.896909	+	0.442214i	$0.145807\pi$
$350$	2.38243	−	1.26180i	0.127346	−	0.0674458i
$351$	3.17009			0.169207
$352$			5.26180i			0.280455i
$353$		−	1.86991i		−	0.0995251i	−0.998761	−	0.0497625i	$-0.984154\pi$
$353$		−	1.86991i		−	0.0995251i	0.998761	−	0.0497625i	$-0.0158465\pi$
$354$	2.40522			0.127836
$355$	−25.3184	+	6.29072i	−1.34376	+	0.333877i
$356$	19.5402			1.03563
$357$		−	2.70928i		−	0.143390i
$358$			10.4429i			0.551927i
$359$	−1.98667			−0.104852			−0.0524262	−	0.998625i	$-0.516695\pi$
$359$	−1.98667			−0.104852			−0.0524262	+	0.998625i	$0.516695\pi$
$360$	1.07838	+	4.34017i	0.0568355	+	0.228747i
$361$	−7.84324			−0.412802
$362$			5.77310i			0.303427i
$363$			1.00000i			0.0524864i
$364$	−5.41855			−0.284009
$365$	3.73206	+	15.0205i	0.195345	+	0.786210i
$366$	−4.01560			−0.209899
$367$		−	29.0300i		−	1.51535i	−0.652631	−	0.757676i	$-0.726335\pi$
$367$		−	29.0300i		−	1.51535i	0.652631	−	0.757676i	$-0.273665\pi$
$368$			3.81658i			0.198953i
$369$	0.829914			0.0432036
$370$	3.70928	−	0.921622i	0.192836	−	0.0479129i
$371$	5.92162			0.307435
$372$			8.92162i			0.462565i
$373$			21.6381i			1.12038i	0.828365	+	0.560189i	$0.189271\pi$
$373$			21.6381i			1.12038i	−0.828365	+	0.560189i	$0.810729\pi$
$374$	−1.46081			−0.0755367
$375$	7.46081	+	8.32684i	0.385275	+	0.429996i
$376$	−9.75872			−0.503268
$377$		−	3.95774i		−	0.203834i
$378$		−	0.539189i		−	0.0277329i
$379$	−11.4163			−0.586415			−0.293208	−	0.956049i	$-0.594723\pi$
$379$	−11.4163			−0.586415			−0.293208	+	0.956049i	$0.594723\pi$
$380$	12.3896	−	3.07838i	0.635574	−	0.157917i
$381$	−7.14116			−0.365853
$382$			10.0410i			0.513744i
$383$			17.8010i			0.909588i	0.890597	+	0.454794i	$0.150287\pi$
$383$			17.8010i			0.909588i	−0.890597	+	0.454794i	$0.849713\pi$
$384$	11.5174			0.587747
$385$	−0.539189	−	2.17009i	−0.0274796	−	0.110598i
$386$	7.96880			0.405601
$387$			1.24846i			0.0634630i
$388$			7.39576i			0.375463i
$389$	−17.7659			−0.900767			−0.450384	−	0.892835i	$-0.648713\pi$
$389$	−17.7659			−0.900767			−0.450384	+	0.892835i	$0.648713\pi$
$390$	0.921622	+	3.70928i	0.0466682	+	0.187826i
$391$	−4.41855			−0.223456
$392$			2.00000i			0.101015i
$393$		−	2.09171i		−	0.105513i
$394$	10.2946			0.518634
$395$	−20.0072	+	4.97107i	−1.00667	+	0.250122i
$396$	1.70928			0.0858943
$397$			12.2907i			0.616854i	0.951248	+	0.308427i	$0.0998025\pi$
$397$			12.2907i			0.616854i	−0.951248	+	0.308427i	$0.900197\pi$
$398$		−	13.1773i		−	0.660517i
$399$	−3.34017			−0.167218
$400$	10.3402	−	5.47641i	0.517009	−	0.273820i
$401$	8.79872			0.439387			0.219693	−	0.975569i	$-0.429494\pi$
$401$	8.79872			0.439387			0.219693	+	0.975569i	$0.429494\pi$
$402$			1.07838i			0.0537846i
$403$			16.5464i			0.824234i
$404$	4.58145			0.227936
$405$	2.17009	−	0.539189i	0.107832	−	0.0267925i
$406$	−0.673158			−0.0334083
$407$		−	3.17009i		−	0.157135i
$408$			5.41855i			0.268258i
$409$	−7.65142			−0.378338			−0.189169	−	0.981945i	$-0.560579\pi$
$409$	−7.65142			−0.378338			−0.189169	+	0.981945i	$0.560579\pi$
$410$	0.241276	+	0.971071i	0.0119158	+	0.0479578i
$411$	11.2846			0.556627
$412$		−	15.3958i		−	0.758495i
$413$			4.46081i			0.219502i
$414$	−0.879362			−0.0432183
$415$	−8.11450	−	32.6586i	−0.398325	−	1.60315i
$416$	16.6803			0.817821
$417$		−	19.9916i		−	0.978992i
$418$			1.80098i			0.0880890i
$419$	35.8710			1.75241			0.876205	−	0.481938i	$-0.160067\pi$
$419$	35.8710			1.75241			0.876205	+	0.481938i	$0.160067\pi$
$420$	−3.70928	+	0.921622i	−0.180994	+	0.0449706i
$421$	−10.2351			−0.498830			−0.249415	−	0.968397i	$-0.580238\pi$
$421$	−10.2351			−0.498830			−0.249415	+	0.968397i	$0.580238\pi$
$422$			12.0000i			0.584151i
$423$			4.87936i			0.237243i
$424$	−11.8432			−0.575159
$425$	6.34017	+	11.9711i	0.307544	+	0.580682i
$426$	−6.29072			−0.304787
$427$		−	7.44748i		−	0.360409i
$428$			16.7526i			0.809767i
$429$	3.17009			0.153053
$430$	−1.46081	+	0.362959i	−0.0704466	+	0.0175035i
$431$	−29.9565			−1.44295			−0.721477	−	0.692438i	$-0.756537\pi$
$431$	−29.9565			−1.44295			−0.721477	+	0.692438i	$0.756537\pi$
$432$		−	2.34017i		−	0.112592i
$433$		−	31.8264i		−	1.52948i	−0.644339	−	0.764740i	$-0.722867\pi$
$433$		−	31.8264i		−	1.52948i	0.644339	−	0.764740i	$-0.277133\pi$
$434$	2.81432			0.135091
$435$	−0.673158	−	2.70928i	−0.0322755	−	0.129900i
$436$	21.0205			1.00670
$437$			5.44748i			0.260588i
$438$			3.73206i			0.178325i
$439$	13.7792			0.657647			0.328824	−	0.944391i	$-0.393348\pi$
$439$	13.7792			0.657647			0.328824	+	0.944391i	$0.393348\pi$
$440$	1.07838	+	4.34017i	0.0514096	+	0.206910i
$441$	1.00000			0.0476190
$442$			4.63090i			0.220269i
$443$			0.573039i			0.0272259i	0.999907	+	0.0136129i	$0.00433327\pi$
$443$			0.573039i			0.0272259i	−0.999907	+	0.0136129i	$0.995667\pi$
$444$	−5.41855			−0.257153
$445$	24.8082	−	6.16394i	1.17602	−	0.292199i
$446$	−13.0400			−0.617462
$447$		−	10.0000i		−	0.472984i
$448$			1.84324i			0.0870851i
$449$	14.2751			0.673685			0.336842	−	0.941561i	$-0.390641\pi$
$449$	14.2751			0.673685			0.336842	+	0.941561i	$0.390641\pi$
$450$	1.26180	+	2.38243i	0.0594816	+	0.112309i
$451$	0.829914			0.0390791
$452$		−	21.9916i		−	1.03440i
$453$		−	3.26180i		−	0.153253i
$454$	−13.9844			−0.656320
$455$	−6.87936	+	1.70928i	−0.322509	+	0.0801321i
$456$	6.68035			0.312836
$457$			12.9350i			0.605072i	0.953138	+	0.302536i	$0.0978332\pi$
$457$			12.9350i			0.605072i	−0.953138	+	0.302536i	$0.902167\pi$
$458$			0.505339i			0.0236129i
$459$	2.70928			0.126458
$460$	1.50307	+	6.04945i	0.0700811	+	0.282057i
$461$	22.7070			1.05757			0.528785	−	0.848756i	$-0.322648\pi$
$461$	22.7070			1.05757			0.528785	+	0.848756i	$0.322648\pi$
$462$		−	0.539189i		−	0.0250853i
$463$			4.29914i			0.199798i	0.994998	+	0.0998989i	$0.0318519\pi$
$463$			4.29914i			0.199798i	−0.994998	+	0.0998989i	$0.968148\pi$
$464$	−2.92162			−0.135633
$465$	2.81432	+	11.3268i	0.130511	+	0.525270i
$466$	9.42243			0.436485
$467$		−	24.8371i		−	1.14932i	−0.818391	−	0.574662i	$-0.805134\pi$
$467$		−	24.8371i		−	1.14932i	0.818391	−	0.574662i	$-0.194866\pi$
$468$		−	5.41855i		−	0.250473i
$469$	−2.00000			−0.0923514
$470$	−5.70928	+	1.41855i	−0.263349	+	0.0654329i
$471$	−8.06278			−0.371513
$472$		−	8.92162i		−	0.410651i
$473$			1.24846i			0.0574044i
$474$	−4.97107			−0.228329
$475$	14.7587	−	7.81658i	0.677177	−	0.358649i
$476$	−4.63090			−0.212257
$477$			5.92162i			0.271132i
$478$			7.03224i			0.321647i
$479$	19.9350			0.910851			0.455426	−	0.890274i	$-0.349487\pi$
$479$	19.9350			0.910851			0.455426	+	0.890274i	$0.349487\pi$
$480$	11.4186	−	2.83710i	0.521183	−	0.129495i
$481$	−10.0494			−0.458215
$482$			10.0312i			0.456908i
$483$		−	1.63090i		−	0.0742084i
$484$	1.70928			0.0776943
$485$	2.33299	+	9.38962i	0.105935	+	0.426361i
$486$	0.539189			0.0244581
$487$		−	34.9048i		−	1.58169i	−0.612018	−	0.790844i	$-0.709642\pi$
$487$		−	34.9048i		−	1.58169i	0.612018	−	0.790844i	$-0.290358\pi$
$488$			14.8950i			0.674263i
$489$	−3.17009			−0.143356
$490$	0.290725	+	1.17009i	0.0131336	+	0.0528591i
$491$	28.6853			1.29455			0.647274	−	0.762257i	$-0.275909\pi$
$491$	28.6853			1.29455			0.647274	+	0.762257i	$0.275909\pi$
$492$		−	1.41855i		−	0.0639532i
$493$		−	3.38243i		−	0.152337i
$494$	5.70928			0.256872
$495$	2.17009	−	0.539189i	0.0975381	−	0.0242347i
$496$	12.2146			0.548452
$497$		−	11.6670i		−	0.523337i
$498$		−	8.11450i		−	0.363619i
$499$	−15.4040			−0.689578			−0.344789	−	0.938680i	$-0.612049\pi$
$499$	−15.4040			−0.689578			−0.344789	+	0.938680i	$0.612049\pi$
$500$	14.2329	−	12.7526i	0.636513	−	0.570313i
$501$	4.20620			0.187919
$502$			1.19165i			0.0531860i
$503$			5.49693i			0.245096i	0.992463	+	0.122548i	$0.0391065\pi$
$503$			5.49693i			0.245096i	−0.992463	+	0.122548i	$0.960893\pi$
$504$	−2.00000			−0.0890871
$505$	5.81658	−	1.44521i	0.258835	−	0.0643111i
$506$	−0.879362			−0.0390924
$507$			2.95055i			0.131039i
$508$			12.2062i			0.541563i
$509$	−24.8381			−1.10093			−0.550466	−	0.834858i	$-0.685550\pi$
$509$	−24.8381			−1.10093			−0.550466	+	0.834858i	$0.685550\pi$
$510$	0.787653	+	3.17009i	0.0348779	+	0.140374i
$511$	−6.92162			−0.306195
$512$		−	21.6742i		−	0.957873i
$513$		−	3.34017i		−	0.147472i
$514$	0.649808			0.0286618
$515$	−4.85658	−	19.5464i	−0.214006	−	0.861316i
$516$	2.13397			0.0939428
$517$			4.87936i			0.214594i
$518$			1.70928i			0.0751012i
$519$	−2.65756			−0.116654
$520$	13.7587	−	3.41855i	0.603360	−	0.149913i
$521$	−13.0300			−0.570854			−0.285427	−	0.958401i	$-0.592135\pi$
$521$	−13.0300			−0.570854			−0.285427	+	0.958401i	$0.592135\pi$
$522$		−	0.673158i		−	0.0294633i
$523$			21.6020i			0.944588i	0.881441	+	0.472294i	$0.156574\pi$
$523$			21.6020i			0.944588i	−0.881441	+	0.472294i	$0.843426\pi$
$524$	−3.57531			−0.156188
$525$	−4.41855	+	2.34017i	−0.192841	+	0.102134i
$526$	−6.38575			−0.278432
$527$			14.1412i			0.615998i
$528$		−	2.34017i		−	0.101843i
$529$	20.3402			0.884355
$530$	−6.92881	+	1.72156i	−0.300968	+	0.0747799i
$531$	−4.46081			−0.193583
$532$			5.70928i			0.247528i
$533$		−	2.63090i		−	0.113957i
$534$	6.16394			0.266740
$535$	5.28458	+	21.2690i	0.228472	+	0.919538i
$536$	4.00000			0.172774
$537$		−	19.3679i		−	0.835786i
$538$		−	12.7142i		−	0.548148i
$539$	1.00000			0.0430730
$540$	−0.921622	−	3.70928i	−0.0396603	−	0.159622i
$541$	−27.5285			−1.18354			−0.591772	−	0.806106i	$-0.701571\pi$
$541$	−27.5285			−1.18354			−0.591772	+	0.806106i	$0.701571\pi$
$542$			5.39067i			0.231549i
$543$		−	10.7070i		−	0.459482i
$544$	14.2557			0.611206
$545$	26.6875	−	6.63090i	1.14317	−	0.284036i
$546$	−1.70928			−0.0731502
$547$		−	37.8625i		−	1.61889i	−0.587199	−	0.809443i	$-0.699769\pi$
$547$		−	37.8625i		−	1.61889i	0.587199	−	0.809443i	$-0.300231\pi$
$548$		−	19.2885i		−	0.823962i
$549$	7.44748			0.317851
$550$	1.26180	+	2.38243i	0.0538031	+	0.101587i
$551$	−4.17009			−0.177652
$552$			3.26180i			0.138831i
$553$		−	9.21953i		−	0.392055i
$554$	−16.1034			−0.684169
$555$	−6.87936	+	1.70928i	−0.292013	+	0.0725547i
$556$	−34.1711			−1.44918
$557$			5.86991i			0.248716i	0.992237	+	0.124358i	$0.0396871\pi$
$557$			5.86991i			0.248716i	−0.992237	+	0.124358i	$0.960313\pi$
$558$			2.81432i			0.119139i
$559$	3.95774			0.167395
$560$	1.26180	+	5.07838i	0.0533206	+	0.214601i
$561$	2.70928			0.114386
$562$			9.63317i			0.406351i
$563$		−	10.4163i		−	0.438994i	−0.975613	−	0.219497i	$-0.929558\pi$
$563$		−	10.4163i		−	0.438994i	0.975613	−	0.219497i	$-0.0704416\pi$
$564$	8.34017			0.351185
$565$	−6.93722	−	27.9204i	−0.291851	−	1.17462i
$566$	−2.45977			−0.103392
$567$			1.00000i			0.0419961i
$568$			23.3340i			0.979074i
$569$	22.9532			0.962248			0.481124	−	0.876652i	$-0.340229\pi$
$569$	22.9532			0.962248			0.481124	+	0.876652i	$0.340229\pi$
$570$	3.90829	−	0.971071i	0.163700	−	0.0406737i
$571$	37.8154			1.58252			0.791262	−	0.611478i	$-0.209425\pi$
$571$	37.8154			1.58252			0.791262	+	0.611478i	$0.209425\pi$
$572$		−	5.41855i		−	0.226561i
$573$		−	18.6225i		−	0.777966i
$574$	−0.447480			−0.0186775
$575$	3.81658	+	7.20620i	0.159162	+	0.300519i
$576$	−1.84324			−0.0768019
$577$		−	32.7070i		−	1.36161i	−0.732464	−	0.680805i	$-0.761630\pi$
$577$		−	32.7070i		−	1.36161i	0.732464	−	0.680805i	$-0.238370\pi$
$578$		−	5.20847i		−	0.216644i
$579$	−14.7792			−0.614204
$580$	−4.63090	+	1.15061i	−0.192288	+	0.0477766i
$581$	15.0494			0.624356
$582$			2.33299i			0.0967053i
$583$			5.92162i			0.245249i
$584$	13.8432			0.572838
$585$	−1.70928	−	6.87936i	−0.0706698	−	0.284427i
$586$	−8.09558			−0.334426
$587$			36.2979i			1.49818i	0.662471	+	0.749088i	$0.269508\pi$
$587$			36.2979i			1.49818i	−0.662471	+	0.749088i	$0.730492\pi$
$588$		−	1.70928i		−	0.0704893i
$589$	17.4341			0.718362
$590$	−1.29687	−	5.21953i	−0.0533912	−	0.214885i
$591$	−19.0928			−0.785371
$592$			7.41855i			0.304901i
$593$			2.78765i			0.114475i	0.998361	+	0.0572376i	$0.0182293\pi$
$593$			2.78765i			0.114475i	−0.998361	+	0.0572376i	$0.981771\pi$
$594$	0.539189			0.0221232
$595$	−5.87936	+	1.46081i	−0.241030	+	0.0598874i
$596$	−17.0928			−0.700146
$597$			24.4391i			1.00022i
$598$			2.78765i			0.113996i
$599$	18.9627			0.774793			0.387397	−	0.921913i	$-0.373374\pi$
$599$	18.9627			0.774793			0.387397	+	0.921913i	$0.373374\pi$
$600$	8.83710	−	4.68035i	0.360773	−	0.191074i
$601$	19.5464			0.797313			0.398657	−	0.917100i	$-0.369477\pi$
$601$	19.5464			0.797313			0.398657	+	0.917100i	$0.369477\pi$
$602$		−	0.673158i		−	0.0274359i
$603$		−	2.00000i		−	0.0814463i
$604$	−5.57531			−0.226856
$605$	2.17009	−	0.539189i	0.0882266	−	0.0219211i
$606$	1.44521			0.0587078
$607$			10.3935i			0.421859i	0.977501	+	0.210930i	$0.0676491\pi$
$607$			10.3935i			0.421859i	−0.977501	+	0.210930i	$0.932351\pi$
$608$		−	17.5753i		−	0.712773i
$609$	1.24846			0.0505903
$610$	2.16517	+	8.71420i	0.0876650	+	0.352827i
$611$	15.4680			0.625768
$612$		−	4.63090i		−	0.187193i
$613$		−	1.65529i		−	0.0668566i	−0.999441	−	0.0334283i	$-0.989357\pi$
$613$		−	1.65529i		−	0.0668566i	0.999441	−	0.0334283i	$-0.0106425\pi$
$614$	−11.1362			−0.449422
$615$	−0.447480	−	1.80098i	−0.0180441	−	0.0726227i
$616$	−2.00000			−0.0805823
$617$			28.4931i			1.14709i	0.819175	+	0.573544i	$0.194432\pi$
$617$			28.4931i			1.14709i	−0.819175	+	0.573544i	$0.805568\pi$
$618$		−	4.85658i		−	0.195360i
$619$	−25.8843			−1.04038			−0.520189	−	0.854051i	$-0.674138\pi$
$619$	−25.8843			−1.04038			−0.520189	+	0.854051i	$0.674138\pi$
$620$	19.3607	−	4.81044i	0.777544	−	0.193192i
$621$	1.63090			0.0654457
$622$			12.4826i			0.500505i
$623$			11.4319i			0.458009i
$624$	−7.41855			−0.296980
$625$	14.0472	−	20.6803i	0.561887	−	0.827214i
$626$	13.9928			0.559265
$627$		−	3.34017i		−	0.133394i
$628$			13.7815i			0.549942i
$629$	−8.58864			−0.342451
$630$	−1.17009	+	0.290725i	−0.0466174	+	0.0115827i
$631$	39.3318			1.56577			0.782886	−	0.622165i	$-0.213747\pi$
$631$	39.3318			1.56577			0.782886	+	0.622165i	$0.213747\pi$
$632$			18.4391i			0.733467i
$633$		−	22.2557i		−	0.884583i
$634$	3.81205			0.151396
$635$	3.85043	+	15.4969i	0.152800	+	0.614977i
$636$	10.1217			0.401351
$637$		−	3.17009i		−	0.125603i
$638$		−	0.673158i		−	0.0266506i
$639$	11.6670			0.461540
$640$	−6.21008	−	24.9939i	−0.245475	−	0.987969i
$641$	−25.3028			−0.999402			−0.499701	−	0.866198i	$-0.666557\pi$
$641$	−25.3028			−0.999402			−0.499701	+	0.866198i	$0.666557\pi$
$642$			5.28458i			0.208566i
$643$			42.6053i			1.68019i	0.542441	+	0.840094i	$0.317500\pi$
$643$			42.6053i			1.68019i	−0.542441	+	0.840094i	$0.682500\pi$
$644$	−2.78765			−0.109849
$645$	2.70928	−	0.673158i	0.106678	−	0.0265056i
$646$	4.87936			0.191976
$647$			34.6369i			1.36172i	0.732416	+	0.680858i	$0.238393\pi$
$647$			34.6369i			1.36172i	−0.732416	+	0.680858i	$0.761607\pi$
$648$		−	2.00000i		−	0.0785674i
$649$	−4.46081			−0.175102
$650$	7.55252	−	4.00000i	0.296234	−	0.156893i
$651$	−5.21953			−0.204570
$652$			5.41855i			0.212207i
$653$		−	1.94828i		−	0.0762423i	−0.999273	−	0.0381211i	$-0.987863\pi$
$653$		−	1.94828i		−	0.0762423i	0.999273	−	0.0381211i	$-0.0121373\pi$
$654$	6.63090			0.259289
$655$	−4.53919	+	1.12783i	−0.177361	+	0.0440678i
$656$	−1.94214			−0.0758279
$657$		−	6.92162i		−	0.270038i
$658$		−	2.63090i		−	0.102563i
$659$	0.506384			0.0197259			0.00986296	−	0.999951i	$-0.496860\pi$
$659$	0.506384			0.0197259			0.00986296	+	0.999951i	$0.496860\pi$
$660$	−0.921622	−	3.70928i	−0.0358741	−	0.144383i
$661$	23.0316			0.895825			0.447912	−	0.894077i	$-0.352168\pi$
$661$	23.0316			0.895825			0.447912	+	0.894077i	$0.352168\pi$
$662$		−	0.683658i		−	0.0265711i
$663$		−	8.58864i		−	0.333555i
$664$	−30.0989			−1.16806
$665$	1.80098	+	7.24846i	0.0698392	+	0.281083i
$666$	−1.70928			−0.0662331
$667$		−	2.03612i		−	0.0788388i
$668$		−	7.18956i		−	0.278172i
$669$	24.1845			0.935025
$670$	2.34017	−	0.581449i	0.0904088	−	0.0224633i
$671$	7.44748			0.287507
$672$			5.26180i			0.202978i
$673$			17.4280i			0.671800i	0.941898	+	0.335900i	$0.109040\pi$
$673$			17.4280i			0.671800i	−0.941898	+	0.335900i	$0.890960\pi$
$674$	1.35350			0.0521350
$675$	−2.34017	−	4.41855i	−0.0900733	−	0.170070i
$676$	5.04331			0.193973
$677$			13.0183i			0.500332i	0.968203	+	0.250166i	$0.0804852\pi$
$677$			13.0183i			0.500332i	−0.968203	+	0.250166i	$0.919515\pi$
$678$		−	6.93722i		−	0.266422i
$679$	−4.32684			−0.166049
$680$	11.7587	−	2.92162i	0.450926	−	0.112039i
$681$	25.9360			0.993870
$682$			2.81432i			0.107766i
$683$		−	25.4764i		−	0.974828i	−0.873171	−	0.487414i	$-0.837940\pi$
$683$		−	25.4764i		−	0.974828i	0.873171	−	0.487414i	$-0.162060\pi$
$684$	−5.70928			−0.218300
$685$	−6.08452	−	24.4885i	−0.232478	−	0.935658i
$686$	−0.539189			−0.0205863
$687$		−	0.937221i		−	0.0357572i
$688$		−	2.92162i		−	0.111386i
$689$	18.7721			0.715158
$690$	0.474142	+	1.90829i	0.0180503	+	0.0726474i
$691$	34.6635			1.31866			0.659331	−	0.751853i	$-0.270839\pi$
$691$	34.6635			1.31866			0.659331	+	0.751853i	$0.270839\pi$
$692$			4.54250i			0.172680i
$693$			1.00000i			0.0379869i
$694$	0.909336			0.0345179
$695$	−43.3835	+	10.7792i	−1.64563	+	0.408880i
$696$	−2.49693			−0.0946458
$697$		−	2.24846i		−	0.0851667i
$698$		−	18.0689i		−	0.683919i
$699$	−17.4752			−0.660972
$700$	4.00000	+	7.55252i	0.151186	+	0.285458i
$701$	15.4007			0.581676			0.290838	−	0.956772i	$-0.406066\pi$
$701$	15.4007			0.581676			0.290838	+	0.956772i	$0.406066\pi$
$702$		−	1.70928i		−	0.0645124i
$703$			10.5886i			0.399358i
$704$	−1.84324			−0.0694699
$705$	10.5886	−	2.63090i	0.398791	−	0.0990853i
$706$	−1.00823			−0.0379453
$707$			2.68035i			0.100805i
$708$			7.62475i			0.286556i
$709$	30.2123			1.13465			0.567324	−	0.823495i	$-0.307979\pi$
$709$	30.2123			1.13465			0.567324	+	0.823495i	$0.307979\pi$
$710$	3.39189	+	13.6514i	0.127295	+	0.512329i
$711$	9.21953			0.345760
$712$		−	22.8638i		−	0.856856i
$713$			8.51253i			0.318797i
$714$	−1.46081			−0.0546695
$715$	−1.70928	−	6.87936i	−0.0639233	−	0.257274i
$716$	−33.1050			−1.23719
$717$		−	13.0423i		−	0.487072i
$718$			1.07119i			0.0399764i
$719$	−35.7514			−1.33330			−0.666650	−	0.745371i	$-0.732273\pi$
$719$	−35.7514			−1.33330			−0.666650	+	0.745371i	$0.732273\pi$
$720$	−5.07838	+	1.26180i	−0.189260	+	0.0470243i
$721$	9.00719			0.335445
$722$			4.22899i			0.157387i
$723$		−	18.6042i		−	0.691899i
$724$	−18.3012			−0.680160
$725$	−5.51640	+	2.92162i	−0.204874	+	0.108506i
$726$	0.539189			0.0200112
$727$		−	22.6319i		−	0.839372i	−0.907669	−	0.419686i	$-0.862140\pi$
$727$		−	22.6319i		−	0.839372i	0.907669	−	0.419686i	$-0.137860\pi$
$728$			6.34017i			0.234982i
$729$	−1.00000			−0.0370370
$730$	8.09890	−	2.01229i	0.299754	−	0.0744781i
$731$	3.38243			0.125104
$732$		−	12.7298i		−	0.470507i
$733$			27.8987i			1.03046i	0.857052	+	0.515230i	$0.172294\pi$
$733$			27.8987i			1.03046i	−0.857052	+	0.515230i	$0.827706\pi$
$734$	−15.6526			−0.577749
$735$	−0.539189	−	2.17009i	−0.0198883	−	0.0800448i
$736$	8.58145			0.316316
$737$		−	2.00000i		−	0.0736709i
$738$		−	0.447480i		−	0.0164720i
$739$	−3.60650			−0.132667			−0.0663337	−	0.997797i	$-0.521130\pi$
$739$	−3.60650			−0.132667			−0.0663337	+	0.997797i	$0.521130\pi$
$740$	2.92162	+	11.7587i	0.107401	+	0.432259i
$741$	−10.5886			−0.388983
$742$		−	3.19287i		−	0.117214i
$743$		−	7.83096i		−	0.287290i	−0.989629	−	0.143645i	$-0.954118\pi$
$743$		−	7.83096i		−	0.287290i	0.989629	−	0.143645i	$-0.0458823\pi$
$744$	10.4391			0.382715
$745$	−21.7009	+	5.39189i	−0.795058	+	0.197544i
$746$	11.6670			0.427160
$747$			15.0494i			0.550631i
$748$		−	4.63090i		−	0.169322i
$749$	−9.80098			−0.358120
$750$	4.48974	−	4.02279i	0.163942	−	0.146891i
$751$	−19.6803			−0.718146			−0.359073	−	0.933309i	$-0.616907\pi$
$751$	−19.6803			−0.718146			−0.359073	+	0.933309i	$0.616907\pi$
$752$		−	11.4186i		−	0.416392i
$753$		−	2.21008i		−	0.0805398i
$754$	−2.13397			−0.0777146
$755$	−7.07838	+	1.75872i	−0.257609	+	0.0640065i
$756$	1.70928			0.0621657
$757$		−	8.11327i		−	0.294882i	−0.989071	−	0.147441i	$-0.952896\pi$
$757$		−	8.11327i		−	0.294882i	0.989071	−	0.147441i	$-0.0471036\pi$
$758$			6.15553i			0.223579i
$759$	1.63090			0.0591978
$760$	−3.60197	−	14.4969i	−0.130657	−	0.525859i
$761$	12.2967			0.445755			0.222877	−	0.974846i	$-0.428455\pi$
$761$	12.2967			0.445755			0.222877	+	0.974846i	$0.428455\pi$
$762$			3.85043i			0.139486i
$763$			12.2979i			0.445214i
$764$	−31.8310			−1.15160
$765$	−1.46081	−	5.87936i	−0.0528157	−	0.212569i
$766$	9.59809			0.346793
$767$			14.1412i			0.510608i
$768$		−	2.52359i		−	0.0910622i
$769$	28.3028			1.02063			0.510313	−	0.859989i	$-0.329530\pi$
$769$	28.3028			1.02063			0.510313	+	0.859989i	$0.329530\pi$
$770$	−1.17009	+	0.290725i	−0.0421670	+	0.0104770i
$771$	−1.20516			−0.0434027
$772$			25.2618i			0.909192i
$773$			54.9914i			1.97790i	0.148237	+	0.988952i	$0.452640\pi$
$773$			54.9914i			1.97790i	−0.148237	+	0.988952i	$0.547360\pi$
$774$	0.673158			0.0241962
$775$	23.0628	−	12.2146i	0.828439	−	0.438762i
$776$	8.65368			0.310649
$777$		−	3.17009i		−	0.113726i
$778$			9.57918i			0.343430i
$779$	−2.77205			−0.0993192
$780$	−11.7587	+	2.92162i	−0.421030	+	0.104611i
$781$	11.6670			0.417479
$782$			2.38243i			0.0851956i
$783$			1.24846i			0.0446165i
$784$	−2.34017			−0.0835776
$785$	4.34736	+	17.4969i	0.155164	+	0.624492i
$786$	−1.12783			−0.0402282
$787$			11.3028i			0.402902i	0.979499	+	0.201451i	$0.0645658\pi$
$787$			11.3028i			0.402902i	−0.979499	+	0.201451i	$0.935434\pi$
$788$			32.6348i			1.16257i
$789$	11.8432			0.421631
$790$	2.68035	+	10.7877i	0.0953624	+	0.383807i
$791$	12.8660			0.457463
$792$		−	2.00000i		−	0.0710669i
$793$		−	23.6092i		−	0.838386i
$794$	6.62702			0.235184
$795$	12.8504	−	3.19287i	0.455758	−	0.113240i
$796$	41.7731			1.48061
$797$			52.5380i			1.86099i	0.366304	+	0.930495i	$0.380623\pi$
$797$			52.5380i			1.86099i	−0.366304	+	0.930495i	$0.619377\pi$
$798$			1.80098i			0.0637541i
$799$	13.2195			0.467674
$800$	−12.3135	−	23.2495i	−0.435348	−	0.821994i
$801$	−11.4319			−0.403926
$802$		−	4.74417i		−	0.167522i
$803$		−	6.92162i		−	0.244259i
$804$	−3.41855			−0.120563
$805$	−3.53919	+	0.879362i	−0.124740	+	0.0309934i
$806$	8.92162			0.314251
$807$			23.5802i			0.830063i
$808$		−	5.36069i		−	0.188588i
$809$	−21.6163			−0.759990			−0.379995	−	0.924989i	$-0.624074\pi$
$809$	−21.6163			−0.759990			−0.379995	+	0.924989i	$0.624074\pi$
$810$	−0.290725	−	1.17009i	−0.0102150	−	0.0411126i
$811$	27.9611			0.981845			0.490923	−	0.871203i	$-0.336660\pi$
$811$	27.9611			0.981845			0.490923	+	0.871203i	$0.336660\pi$
$812$		−	2.13397i		−	0.0748876i
$813$		−	9.99773i		−	0.350636i
$814$	−1.70928			−0.0599101
$815$	1.70928	+	6.87936i	0.0598733	+	0.240974i
$816$	−6.34017			−0.221950
$817$		−	4.17009i		−	0.145893i
$818$			4.12556i			0.144247i
$819$	3.17009			0.110772
$820$	−3.07838	+	0.764867i	−0.107502	+	0.0267103i
$821$	25.0710			0.874984			0.437492	−	0.899222i	$-0.355867\pi$
$821$	25.0710			0.874984			0.437492	+	0.899222i	$0.355867\pi$
$822$		−	6.08452i		−	0.212222i
$823$			51.6502i			1.80041i	0.435464	+	0.900206i	$0.356584\pi$
$823$			51.6502i			1.80041i	−0.435464	+	0.900206i	$0.643416\pi$
$824$	−18.0144			−0.627561
$825$	−2.34017	−	4.41855i	−0.0814744	−	0.153834i
$826$	2.40522			0.0836883
$827$			45.2039i			1.57189i	0.618293	+	0.785947i	$0.287824\pi$
$827$			45.2039i			1.57189i	−0.618293	+	0.785947i	$0.712176\pi$
$828$		−	2.78765i		−	0.0968776i
$829$	−7.88428			−0.273832			−0.136916	−	0.990583i	$-0.543719\pi$
$829$	−7.88428			−0.273832			−0.136916	+	0.990583i	$0.543719\pi$
$830$	−17.6092	+	4.37525i	−0.611223	+	0.151867i
$831$	29.8660			1.03604
$832$			5.84324i			0.202578i
$833$		−	2.70928i		−	0.0938708i
$834$	−10.7792			−0.373255
$835$	−2.26794	−	9.12783i	−0.0784852	−	0.315881i
$836$	−5.70928			−0.197459
$837$		−	5.21953i		−	0.180414i
$838$		−	19.3412i		−	0.668131i
$839$	−27.4729			−0.948471			−0.474235	−	0.880398i	$-0.657275\pi$
$839$	−27.4729			−0.948471			−0.474235	+	0.880398i	$0.657275\pi$
$840$	1.07838	+	4.34017i	0.0372076	+	0.149750i
$841$	−27.4413			−0.946253
$842$			5.51867i			0.190186i
$843$		−	17.8660i		−	0.615339i
$844$	−38.0410			−1.30943
$845$	6.40295	−	1.59090i	0.220268	−	0.0547288i
$846$	2.63090			0.0904521
$847$			1.00000i			0.0343604i
$848$		−	13.8576i		−	0.475873i
$849$	4.56198			0.156567
$850$	6.45467	−	3.41855i	0.221393	−	0.117255i
$851$	−5.17009			−0.177228
$852$		−	19.9421i		−	0.683206i
$853$			2.85658i			0.0978073i	0.998804	+	0.0489036i	$0.0155727\pi$
$853$			2.85658i			0.0978073i	−0.998804	+	0.0489036i	$0.984427\pi$
$854$	−4.01560			−0.137411
$855$	−7.24846	+	1.80098i	−0.247892	+	0.0615924i
$856$	19.6020			0.669981
$857$			20.4079i			0.697120i	0.937287	+	0.348560i	$0.113329\pi$
$857$			20.4079i			0.697120i	−0.937287	+	0.348560i	$0.886671\pi$
$858$		−	1.70928i		−	0.0583537i
$859$	34.7514			1.18570			0.592851	−	0.805313i	$-0.298002\pi$
$859$	34.7514			1.18570			0.592851	+	0.805313i	$0.298002\pi$
$860$	−1.15061	−	4.63090i	−0.0392356	−	0.157912i
$861$	0.829914			0.0282834
$862$			16.1522i			0.550147i
$863$			50.6619i			1.72455i	0.506439	+	0.862276i	$0.330962\pi$
$863$			50.6619i			1.72455i	−0.506439	+	0.862276i	$0.669038\pi$
$864$	−5.26180			−0.179010
$865$	1.43293	+	5.76713i	0.0487210	+	0.196088i
$866$	−17.1605			−0.583136
$867$			9.65983i			0.328065i
$868$			8.92162i			0.302820i
$869$	9.21953			0.312751
$870$	−1.46081	+	0.362959i	−0.0495261	+	0.0123055i
$871$	−6.34017			−0.214829
$872$		−	24.5958i		−	0.832920i
$873$		−	4.32684i		−	0.146441i
$874$	2.93722			0.0993530
$875$	7.46081	+	8.32684i	0.252221	+	0.281499i
$876$	−11.8310			−0.399731
$877$		−	37.0027i		−	1.24949i	−0.780829	−	0.624745i	$-0.785203\pi$
$877$		−	37.0027i		−	1.24949i	0.780829	−	0.624745i	$-0.214797\pi$
$878$		−	7.42961i		−	0.250737i
$879$	15.0144			0.506422
$880$	−5.07838	+	1.26180i	−0.171192	+	0.0425351i
$881$	−12.0445			−0.405790			−0.202895	−	0.979200i	$-0.565035\pi$
$881$	−12.0445			−0.405790			−0.202895	+	0.979200i	$0.565035\pi$
$882$		−	0.539189i		−	0.0181554i
$883$		−	52.7358i		−	1.77470i	−0.461097	−	0.887350i	$-0.652544\pi$
$883$		−	52.7358i		−	1.77470i	0.461097	−	0.887350i	$-0.347456\pi$
$884$	−14.6803			−0.493753
$885$	2.40522	+	9.68035i	0.0808506	+	0.325401i
$886$	0.308976			0.0103803
$887$		−	14.1362i		−	0.474648i	−0.971431	−	0.237324i	$-0.923730\pi$
$887$		−	14.1362i		−	0.474648i	0.971431	−	0.237324i	$-0.0762704\pi$
$888$			6.34017i			0.212762i
$889$	−7.14116			−0.239507
$890$	−3.32353	−	13.3763i	−0.111405	−	0.448374i
$891$	−1.00000			−0.0335013
$892$		−	41.3379i		−	1.38410i
$893$		−	16.2979i		−	0.545389i
$894$	−5.39189			−0.180332
$895$	−42.0300	+	10.4429i	−1.40491	+	0.349069i
$896$	11.5174			0.384771
$897$		−	5.17009i		−	0.172624i
$898$		−	7.69699i		−	0.256852i
$899$	−6.51640			−0.217334
$900$	−7.55252	+	4.00000i	−0.251751	+	0.133333i
$901$	16.0433			0.534480
$902$		−	0.447480i		−	0.0148995i
$903$			1.24846i			0.0415463i
$904$	−25.7321			−0.855836
$905$	−23.2351	+	5.77310i	−0.772362	+	0.191904i
$906$	−1.75872			−0.0584297
$907$		−	6.47745i		−	0.215080i	−0.994201	−	0.107540i	$-0.965703\pi$
$907$		−	6.47745i		−	0.215080i	0.994201	−	0.107540i	$-0.0342974\pi$
$908$		−	44.3318i		−	1.47120i
$909$	−2.68035			−0.0889015
$910$	0.921622	+	3.70928i	0.0305515	+	0.122961i
$911$	22.5380			0.746716			0.373358	−	0.927687i	$-0.378206\pi$
$911$	22.5380			0.746716			0.373358	+	0.927687i	$0.378206\pi$
$912$			7.81658i			0.258833i
$913$			15.0494i			0.498064i
$914$	6.97438			0.230692
$915$	−4.01560	−	16.1617i	−0.132752	−	0.534289i
$916$	−1.60197			−0.0529305
$917$		−	2.09171i		−	0.0690743i
$918$		−	1.46081i		−	0.0482140i
$919$	21.1773			0.698574			0.349287	−	0.937016i	$-0.386424\pi$
$919$	21.1773			0.698574			0.349287	+	0.937016i	$0.386424\pi$
$920$	7.07838	−	1.75872i	0.233367	−	0.0579834i
$921$	20.6537			0.680562
$922$		−	12.2434i		−	0.403214i
$923$		−	36.9854i		−	1.21739i
$924$	1.70928			0.0562310
$925$	7.41855	+	14.0072i	0.243920	+	0.460554i
$926$	2.31805			0.0761757
$927$			9.00719i			0.295835i
$928$			6.56916i			0.215643i
$929$	−24.4352			−0.801693			−0.400846	−	0.916145i	$-0.631284\pi$
$929$	−24.4352			−0.801693			−0.400846	+	0.916145i	$0.631284\pi$
$930$	6.10731	−	1.51745i	0.200266	−	0.0497591i
$931$	−3.34017			−0.109470
$932$			29.8699i			0.978421i
$933$		−	23.1506i		−	0.757917i
$934$	−13.3919			−0.438196
$935$	−1.46081	−	5.87936i	−0.0477736	−	0.192276i
$936$	−6.34017			−0.207235
$937$		−	18.3063i		−	0.598042i	−0.954247	−	0.299021i	$-0.903340\pi$
$937$		−	18.3063i		−	0.598042i	0.954247	−	0.299021i	$-0.0966600\pi$
$938$			1.07838i			0.0352103i
$939$	−25.9516			−0.846898
$940$	−4.49693	−	18.0989i	−0.146674	−	0.590321i
$941$	−26.7598			−0.872344			−0.436172	−	0.899863i	$-0.643666\pi$
$941$	−26.7598			−0.872344			−0.436172	+	0.899863i	$0.643666\pi$
$942$			4.34736i			0.141645i
$943$		−	1.35350i		−	0.0440762i
$944$	10.4391			0.339763
$945$	2.17009	−	0.539189i	0.0705929	−	0.0175398i
$946$	0.673158			0.0218863
$947$			54.8948i			1.78384i	0.452192	+	0.891920i	$0.350642\pi$
$947$			54.8948i			1.78384i	−0.452192	+	0.891920i	$0.649358\pi$
$948$		−	15.7587i		−	0.511820i
$949$	−21.9421			−0.712272
$950$	−4.21461	−	7.95774i	−0.136740	−	0.258183i
$951$	−7.06997			−0.229259
$952$			5.41855i			0.175616i
$953$			26.5646i			0.860513i	0.902707	+	0.430256i	$0.141577\pi$
$953$			26.5646i			0.860513i	−0.902707	+	0.430256i	$0.858423\pi$
$954$	3.19287			0.103373
$955$	−40.4124	+	10.0410i	−1.30771	+	0.324920i
$956$	−22.2928			−0.721001
$957$			1.24846i			0.0403571i
$958$		−	10.7487i		−	0.347275i
$959$	11.2846			0.364398
$960$	0.993857	+	4.00000i	0.0320766	+	0.129099i
$961$	−3.75646			−0.121176
$962$			5.41855i			0.174701i
$963$		−	9.80098i		−	0.315832i
$964$	−31.7998			−1.02420
$965$	7.96880	+	32.0722i	0.256525	+	1.03244i
$966$	−0.879362			−0.0282930
$967$		−	29.4196i		−	0.946070i	−0.881044	−	0.473035i	$-0.843158\pi$
$967$		−	29.4196i		−	0.946070i	0.881044	−	0.473035i	$-0.156842\pi$
$968$		−	2.00000i		−	0.0642824i
$969$	−9.04945			−0.290710
$970$	5.06278	−	1.25792i	0.162556	−	0.0403894i
$971$	−38.4668			−1.23446			−0.617229	−	0.786784i	$-0.711745\pi$
$971$	−38.4668			−1.23446			−0.617229	+	0.786784i	$0.711745\pi$
$972$			1.70928i			0.0548250i
$973$		−	19.9916i		−	0.640901i
$974$	−18.8203			−0.603041
$975$	−14.0072	+	7.41855i	−0.448589	+	0.237584i
$976$	−17.4284			−0.557869
$977$			14.7464i			0.471780i	0.971780	+	0.235890i	$0.0758006\pi$
$977$			14.7464i			0.471780i	−0.971780	+	0.235890i	$0.924199\pi$
$978$			1.70928i			0.0546566i
$979$	−11.4319			−0.365365
$980$	−3.70928	+	0.921622i	−0.118488	+	0.0294401i
$981$	−12.2979			−0.392642
$982$		−	15.4668i		−	0.493565i
$983$			47.7152i			1.52188i	0.648822	+	0.760940i	$0.275262\pi$
$983$			47.7152i			1.52188i	−0.648822	+	0.760940i	$0.724738\pi$
$984$	−1.65983			−0.0529134
$985$	10.2946	+	41.4329i	0.328013	+	1.32016i
$986$	−1.82377			−0.0580807
$987$			4.87936i			0.155312i
$988$			18.0989i			0.575803i
$989$	2.03612			0.0647448
$990$	−0.290725	−	1.17009i	−0.00923984	−	0.0371878i
$991$	21.9893			0.698514			0.349257	−	0.937027i	$-0.386434\pi$
$991$	21.9893			0.698514			0.349257	+	0.937027i	$0.386434\pi$
$992$		−	27.4641i		−	0.871987i
$993$			1.26794i			0.0402368i
$994$	−6.29072			−0.199530
$995$	53.0349	−	13.1773i	1.68132	−	0.417748i
$996$	25.7237			0.815085
$997$		−	26.4657i		−	0.838178i	−0.907945	−	0.419089i	$-0.862350\pi$
$997$		−	26.4657i		−	0.838178i	0.907945	−	0.419089i	$-0.137650\pi$
$998$			8.30566i			0.262911i
$999$	3.17009			0.100297

Twists

By twisting character
Char	Parity	Ord	Type	Twist	Min	Dim
1.1	even	1	trivial	1155.2.c.c.694.3	✓	6
5.2	odd	4		5775.2.a.bu.1.2		3
5.3	odd	4		5775.2.a.bt.1.2		3
5.4	even	2	inner	1155.2.c.c.694.4	yes	6

By twisted newform
Twist	Min	Dim	Char	Parity	Ord	Type
1155.2.c.c.694.3	✓	6	1.1	even	1	trivial
1155.2.c.c.694.4	yes	6	5.4	even	2	inner
5775.2.a.bt.1.2		3	5.3	odd	4
5775.2.a.bu.1.2		3	5.2	odd	4

Overview	Random
Universe	Knowledge

Classical	Maass
Hilbert	Bianchi

Elliptic curves over $\Q$
Elliptic curves over $\Q(\alpha)$
Genus 2 curves over $\Q$
Higher genus families
Abelian varieties over $\F_{q}$

Level:	\( N \)	\(=\)	\( 1155 = 3 \cdot 5 \cdot 7 \cdot 11 \)
Weight:	\( k \)	\(=\)	\( 2 \)
Character orbit:	\([\chi]\)	\(=\)	1155.c (of order \(2\), degree \(1\), minimal)

\(f(q)\)	\(=\)	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +0.539189 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +O(q^{10})\)	\(q-0.539189i q^{2} +1.00000i q^{3} +1.70928 q^{4} +(2.17009 - 0.539189i) q^{5} +0.539189 q^{6} +1.00000i q^{7} -2.00000i q^{8} -1.00000 q^{9} +(-0.290725 - 1.17009i) q^{10} -1.00000 q^{11} +1.70928i q^{12} +3.17009i q^{13} +0.539189 q^{14} +(0.539189 + 2.17009i) q^{15} +2.34017 q^{16} +2.70928i q^{17} +0.539189i q^{18} +3.34017 q^{19} +(3.70928 - 0.921622i) q^{20} -1.00000 q^{21} +0.539189i q^{22} +1.63090i q^{23} +2.00000 q^{24} +(4.41855 - 2.34017i) q^{25} +1.70928 q^{26} -1.00000i q^{27} +1.70928i q^{28} -1.24846 q^{29} +(1.17009 - 0.290725i) q^{30} +5.21953 q^{31} -5.26180i q^{32} -1.00000i q^{33} +1.46081 q^{34} +(0.539189 + 2.17009i) q^{35} -1.70928 q^{36} +3.17009i q^{37} -1.80098i q^{38} -3.17009 q^{39} +(-1.07838 - 4.34017i) q^{40} -0.829914 q^{41} +0.539189i q^{42} -1.24846i q^{43} -1.70928 q^{44} +(-2.17009 + 0.539189i) q^{45} +0.879362 q^{46} -4.87936i q^{47} +2.34017i q^{48} -1.00000 q^{49} +(-1.26180 - 2.38243i) q^{50} -2.70928 q^{51} +5.41855i q^{52} -5.92162i q^{53} -0.539189 q^{54} +(-2.17009 + 0.539189i) q^{55} +2.00000 q^{56} +3.34017i q^{57} +0.673158i q^{58} +4.46081 q^{59} +(0.921622 + 3.70928i) q^{60} -7.44748 q^{61} -2.81432i q^{62} -1.00000i q^{63} +1.84324 q^{64} +(1.70928 + 6.87936i) q^{65} -0.539189 q^{66} +2.00000i q^{67} +4.63090i q^{68} -1.63090 q^{69} +(1.17009 - 0.290725i) q^{70} -11.6670 q^{71} +2.00000i q^{72} +6.92162i q^{73} +1.70928 q^{74} +(2.34017 + 4.41855i) q^{75} +5.70928 q^{76} -1.00000i q^{77} +1.70928i q^{78} -9.21953 q^{79} +(5.07838 - 1.26180i) q^{80} +1.00000 q^{81} +0.447480i q^{82} -15.0494i q^{83} -1.70928 q^{84} +(1.46081 + 5.87936i) q^{85} -0.673158 q^{86} -1.24846i q^{87} +2.00000i q^{88} +11.4319 q^{89} +(0.290725 + 1.17009i) q^{90} -3.17009 q^{91} +2.78765i q^{92} +5.21953i q^{93} -2.63090 q^{94} +(7.24846 - 1.80098i) q^{95} +5.26180 q^{96} +4.32684i q^{97} +0.539189i q^{98} +1.00000 q^{99} +O(q^{100})\)
\(\operatorname{Tr}(f)(q)\)	\(=\)	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9}+O(q^{10}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9	\( 6 q - 4 q^{4} + 2 q^{5} - 6 q^{9} - 16 q^{10} - 6 q^{11} - 8 q^{16} - 2 q^{19} + 8 q^{20} - 6 q^{21} + 12 q^{24} - 2 q^{25} - 4 q^{26} + 10 q^{29} - 4 q^{30} - 16 q^{31} + 12 q^{34} + 4 q^{36} - 8 q^{39} - 16 q^{41} + 4 q^{44} - 2 q^{45} - 20 q^{46} - 6 q^{49} + 8 q^{50} - 2 q^{51} - 2 q^{55} + 12 q^{56} + 30 q^{59} + 12 q^{60} - 46 q^{61} + 24 q^{64} - 4 q^{65} - 2 q^{69} - 4 q^{70} - 24 q^{71} - 4 q^{74} - 8 q^{75} + 20 q^{76} - 8 q^{79} + 24 q^{80} + 6 q^{81} + 4 q^{84} + 12 q^{85} - 28 q^{86} + 42 q^{89} + 16 q^{90} - 8 q^{91} - 8 q^{94} + 26 q^{95} + 16 q^{96} + 6 q^{99}+O(q^{100}) \) 6 * q - 4 * q^4 + 2 * q^5 - 6 * q^9 - 16 * q^10 - 6 * q^11 - 8 * q^16 - 2 * q^19 + 8 * q^20 - 6 * q^21 + 12 * q^24 - 2 * q^25 - 4 * q^26 + 10 * q^29 - 4 * q^30 - 16 * q^31 + 12 * q^34 + 4 * q^36 - 8 * q^39 - 16 * q^41 + 4 * q^44 - 2 * q^45 - 20 * q^46 - 6 * q^49 + 8 * q^50 - 2 * q^51 - 2 * q^55 + 12 * q^56 + 30 * q^59 + 12 * q^60 - 46 * q^61 + 24 * q^64 - 4 * q^65 - 2 * q^69 - 4 * q^70 - 24 * q^71 - 4 * q^74 - 8 * q^75 + 20 * q^76 - 8 * q^79 + 24 * q^80 + 6 * q^81 + 4 * q^84 + 12 * q^85 - 28 * q^86 + 42 * q^89 + 16 * q^90 - 8 * q^91 - 8 * q^94 + 26 * q^95 + 16 * q^96 + 6 * q^99

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